// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_EULERANGLES_H
#define EIGEN_EULERANGLES_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
  *
  *
  * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
  *
  * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
  * For instance, in:
  * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
  * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
  * we have the following equality:
  * \code
  * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
  *      * AngleAxisf(ea[1], Vector3f::UnitX())
  *      * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
  * This corresponds to the right-multiply conventions (with right hand side frames).
  * 
  * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
  * 
  * \sa class AngleAxis
  */
template <typename Derived>
EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar, 3, 1> MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
{
    EIGEN_USING_STD(atan2)
    EIGEN_USING_STD(sin)
    EIGEN_USING_STD(cos)
    /* Implemented from Graphics Gems IV */
    EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived, 3, 3)

    Matrix<Scalar, 3, 1> res;
    typedef Matrix<typename Derived::Scalar, 2, 1> Vector2;

    const Index odd = ((a0 + 1) % 3 == a1) ? 0 : 1;
    const Index i = a0;
    const Index j = (a0 + 1 + odd) % 3;
    const Index k = (a0 + 2 - odd) % 3;

    if (a0 == a2)
    {
        res[0] = atan2(coeff(j, i), coeff(k, i));
        if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0)))
        {
            if (res[0] > Scalar(0))
            {
                res[0] -= Scalar(EIGEN_PI);
            }
            else
            {
                res[0] += Scalar(EIGEN_PI);
            }
            Scalar s2 = Vector2(coeff(j, i), coeff(k, i)).norm();
            res[1] = -atan2(s2, coeff(i, i));
        }
        else
        {
            Scalar s2 = Vector2(coeff(j, i), coeff(k, i)).norm();
            res[1] = atan2(s2, coeff(i, i));
        }

        // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
        // we can compute their respective rotation, and apply its inverse to M. Since the result must
        // be a rotation around x, we have:
        //
        //  c2  s1.s2 c1.s2                   1  0   0
        //  0   c1    -s1       *    M    =   0  c3  s3
        //  -s2 s1.c2 c1.c2                   0 -s3  c3
        //
        //  Thus:  m11.c1 - m21.s1 = c3  &   m12.c1 - m22.s1 = s3

        Scalar s1 = sin(res[0]);
        Scalar c1 = cos(res[0]);
        res[2] = atan2(c1 * coeff(j, k) - s1 * coeff(k, k), c1 * coeff(j, j) - s1 * coeff(k, j));
    }
    else
    {
        res[0] = atan2(coeff(j, k), coeff(k, k));
        Scalar c2 = Vector2(coeff(i, i), coeff(i, j)).norm();
        if ((odd && res[0] < Scalar(0)) || ((!odd) && res[0] > Scalar(0)))
        {
            if (res[0] > Scalar(0))
            {
                res[0] -= Scalar(EIGEN_PI);
            }
            else
            {
                res[0] += Scalar(EIGEN_PI);
            }
            res[1] = atan2(-coeff(i, k), -c2);
        }
        else
            res[1] = atan2(-coeff(i, k), c2);
        Scalar s1 = sin(res[0]);
        Scalar c1 = cos(res[0]);
        res[2] = atan2(s1 * coeff(k, i) - c1 * coeff(j, i), c1 * coeff(j, j) - s1 * coeff(k, j));
    }
    if (!odd)
        res = -res;

    return res;
}

}  // end namespace Eigen

#endif  // EIGEN_EULERANGLES_H
